The report comes from CalacioMercato, who say the Serie A club are ready to sell the 27-year-old after falling out of Filippo Inzaghi's plans.
According to TuttaBolognaWeb, Rafa Benitez had weighted up a bid for the Italian in the summer having reportedly failed to lure Alassane Plea, Garry Rodrigues and William Jose to St James's Park.
In the end, Benitez secured the loan signing of Salomon Rondon from West Bromwich Albion, who has started in just four Premier League games so far.
Forced to watch Bologna's previous four matches from the bench, it is said Destro is "destined" to leave the club in January - which could see the Magpies re-visit a potential deal.
Speculation yesterday stated Benitez had identified Seb Haller from Eintracht Frankfurt as his prime target. However, should the German club knock back any approaches from Newcastle, a swoop for Destro could be a feasible option.
Destro, who has spent all of his career in Italy since his debut for Genoa in 2010, is likely to be available for a cut-price fee with La Dotta keen to offload him.
The eight-time Italy international, who was scored 66 goals in 206 Serie A appearances, is also said to be attracting the interest of Watford.